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Investigation of $\Lambda_c \to (\Lambda,n)\ell^+ \nu_\ell $ Decays in Standard Model and Beyond

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Standard Model Λc decays run about 10 percent above experiment, and a muon-only scalar operator could close the gap.

desk verdict Solid SM calculation with a complete helicity formalism; the NP section is a benchmark study the abstract overstates as a fit-based prediction. read the letter →

arxiv 2501.12871 v1 pith:HPFVEOUQ submitted 2025-01-22 hep-ph hep-ex

Zhi-Hua Zhang , Ying Li This is my paper · ORCID
classification hep-phhep-ex PACS 12.15.Hh13.30.Ce14.20.Lq
keywords ΛcsemileptonicdecayscharmbaryoneffectiveHamiltonianhelicityamplitudesnewphysicsleptonflavoruniversalitylatticeQCDformfactorsforward-backwardasymmetry
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper studies the weak decays of the charmed baryon Λc into a Λ baryon or a neutron plus a charged lepton and neutrino, using lattice QCD form factors and a model-independent effective Hamiltonian that includes every possible four-fermion operator. The authors find that the Standard Model branching fractions for both channels are approximately 10 percent larger than the current experimental central values, and they examine whether new physics coupling only to muons could explain or alter this pattern. Their key concrete results are that a right-handed scalar operator with Wilson coefficient C_SR = 0.3 can suppress the muonic Λc → Λ and Λc → n branching fractions by up to 10 percent, and that the ratio of forward-backward asymmetries between muon and electron modes is a robust probe because hadronic uncertainties largely cancel in it. The paper also provides a complete set of helicity amplitudes and differential observables that can be compared directly with data from ongoing charmed-baryon experiments.

What carries the argument

The central machinery is the helicity-amplitude decomposition of the three-body decay Λc → (Λ,n)ℓν, built from lattice QCD form factors expanded in the z variable with pole factors defined in Eq. (11). The paper constructs the complete hadronic helicity amplitudes for vector, axial-vector, scalar, pseudoscalar, and tensor operators, matches them to the lepton-side helicity amplitudes, and builds the full differential decay distribution including the interference terms between all pairs of operators. The ratio A_μ/e_FB(q²) is defined in Eq. (101) as the ratio of the muon-mode to electron-mode forward-backward asymmetries, and the claim is that the form-factor uncertainties cancel in this double ratio because numerator and denominator depend on the same hadronic amplitudes.

What would settle it

A measurement of B(Λc → ne+νe) and B(Λc → nμ+νμ) at the 5-10 percent level, combined with an improved measurement of the Λ modes, would directly test the size and sign of the claimed 10 percent offset; if the neutron-mode branching fractions land at the lattice value near 4.1 × 10⁻³ while the Λ modes land at the current central values, the pattern predicted here would not hold. A precise measurement of the ratio A_μ/e_FB in the neutron channel, where tensor form factors are available, would similarly confirm or rule out the claim that this ratio is unaffected by the fitted new physics operators.

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Extended reading notes

Core claim

The paper claims that, using the lattice QCD form factors of Refs. [21] and [45] and the full set of c → (s,d)ℓν effective operators, the Standard Model branching fractions are B(Λc → Λμ+νμ) = (3.75 ± 0.19)%, B(Λc → Λe+νe) = (3.88 ± 0.19)%, B(Λc → nμ+νμ) = (4.05 ± 0.29) × 10⁻³, and B(Λc → ne+νe) = (4.15 ± 0.29) × 10⁻³. These central values sit roughly 10 percent above the experimental measurements of the Λ modes, which are (3.48 ± 0.20)% and (3.56 ± 0.13)%, respectively, although the central values agree within combined uncertainties. For new physics that couples only to the muon, with Wilson coefficients fitted from D and Ds decays, the paper finds that the right-handed scalar operator O_SR, with magnitude 0.3, suppresses the muonic branching fractions by up to 10 percent, and it notes that the sign of the coefficient is negative if the experimental deficit reflects a real new-physics effect. The left-handed vector operator enhances the rates by a similar amount. The paper further claims that the ratio A_μ/e_FB of the muon to electron forward-backward asymmetries is essentially insensitive to the fitted new physics operators and to hadronic form-factor uncertainties, making it a distinctive observable whose measured value should track the Standard Model prediction if no new physics affects this decay.

Load-bearing premise

The lattice QCD form factors from Refs. [21] and [45], including their z-expansion coefficients and quoted uncertainties, are correct; every numerical prediction in the paper inherits that external input, and if the form factors are off by more than their stated errors the 10 percent tension with experiment could disappear or change sign.

Editorial extensions

If this is right

  • If the 10 percent offset between the Standard Model central values and the experimental measurements persists with smaller errors, it would favor a destructive new-physics contribution in the muon channel of the size explored here, rather than a pure Standard Model description.
  • The first observation of Λc → ne+νe, reported after this analysis was completed, gives (3.57 ± 0.34 ± 0.14) × 10⁻³, which is consistent with the paper's prediction and shows the same slight deficit that the Λ modes show, so a common shift in the c → s and c → d channels is worth testing.
  • A precise measurement of the ratio A_μ/e_FB in either the Λ or neutron mode would provide a nearly form-factor-independent test of lepton flavor universality that is complementary to the branching-fraction ratio R_μ/e.
  • The complete set of helicity amplitudes, including all operator interferences, can be reused directly in any future analysis that assumes more than one new physics operator at a time.
  • The tensor operator's effect on the convexity parameter in the Λc → nμ+νμ channel provides a way to distinguish a tensor contribution from the scalar operators, which affect the polarization observables instead.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the same 10 percent suppression pattern appears in both the strangeness-changing and non-strangeness-changing modes, a common new-physics interpretation would need an operator that acts on both c → s and c → d transitions with comparable strength, which is a testable pattern that the paper's single-operator analysis does not yet combine.
  • The paper's A_μ/e_FB ratio could be sharpened by constructing a fully integrated double ratio or a weighted q² average, which would produce a single number with even smaller reported uncertainty and a cleaner experimental target.
  • A future measurement of the neutron-mode branching fractions with 5-percent precision would discriminate between the lattice QCD prediction (around 4.1 × 10⁻³) and the lower quark-model predictions (near 3 × 10⁻³), independently of the new physics question.
  • The absence of tensor form factors for the Λc → Λ transition means the tensor operator's effects are only partially mapped; lattice calculations of those form factors would complete the new-physics reach of this observable set.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies the semileptonic charm-baryon decays Λ_c → (Λ, n)ℓ^+ν_ℓ (ℓ = μ, e) in the Standard Model and in a model-independent effective Hamiltonian with all four-fermion operators. The hadronic helicity amplitudes are derived including interference terms between different NP operators, and the numerical input is the lattice QCD z-expansion form factors of Refs. [21,45]. The SM branching fractions, Eqs. (92)-(93) and (98)-(99), are about 10% above the central experimental values for the Λ modes, although consistent within uncertainties. In the NP section, the paper adopts the Wilson coefficients of Eq. (102), claims that the right-handed scalar operator can suppress the muonic modes by up to 10%, and proposes the ratio of forward-backward asymmetries A_B^{μ/e} as a novel probe that is robust against hadronic uncertainties and largely unaffected by the considered NP operators.

Significance. If the SM predictions are taken at face value, the paper provides a useful, technically complete cross-check of lattice QCD form factors and a possible route to improved |V_cs| and |V_cd| determinations. The helicity-amplitude formalism, including all operator interferences in Appendix A, is a valuable reference for future experimental analyses at BESIII, Belle-II, and LHCb. The SM part of the paper is sound and properly uses published lattice input. However, the advertised NP conclusions are currently overstated: the 'up to 10%' suppression is computed at benchmark coefficients that are not the fitted values invoked in the abstract, and the sign preference statement is internally inconsistent. The proposed forward-backward asymmetry ratio needs a clearer logic if it is to be called a probe of NP.

major comments (3)
  1. [Sec. 3.3, Eq. (102), abstract] The abstract and summary state that the NP predictions use Wilson coefficients 'fitted from D and D_s meson decays,' but the coefficients adopted in Eq. (102) are not the fit results quoted in Sec. 3.3. The text reports fitted values of order 10^{-3} for C_VL and C_VR and 10^{-2} for C_SL and C_SR, with Ref. [56] allowing at most 10^{-1}, and then sets C_SL = C_SR = 0.3 and C_T = 0.15 'in order to maximize the manifestation of NP effects.' Because the dominant NP contribution enters through the VL-SR interference linearly in C_SR, the quoted 'up to 10%' branching-fraction suppression is an upper-bound benchmark, not a prediction. A coefficient within the fitted or allowable ranges would reduce the effect to a few percent or less, placing it inside the form-factor uncertainties of Eqs. (92)-(99). The NP claims should be reframed as sensitivity illustrations, and the abstract should not describe Eq. (102) as arising from fits.
  2. [Sec. 3.3, paragraphs after Fig. 5] There is an internal inconsistency in the sign of the right-handed scalar coefficient. The text says that Figure 5 shows the branching fraction 'suppressed by the right-handed scalar operator O_SR,' with Eq. (102) using positive C_SR = 0.3, but later states that the SM overestimate 'implies that the right-handed scalar operator O_SR with a negative Wilson coefficient is much favored.' If a positive C_SR suppresses the rate, a negative coefficient would enhance it, worsening the overestimate; if a negative coefficient suppresses it, the sign used in Eq. (102) and in the figures cannot produce the advertised suppression. The authors must state explicitly the sign of the VL-SR interference term in Eq. (67) and reconcile the benchmark sign with the preferred-sign conclusion.
  3. [Abstract, Sec. 3.3, Sec. 4] The ratio A_B^{μ/e} of forward-backward asymmetries is presented as a 'novel probe for NP,' yet the paper reports that it is 'largely unaffected by current NP operators.' An observable insensitive to all of the NP operators considered cannot probe those operators; at best it can serve as a cross-check of the SM or as a constraint on operators outside the considered set. The authors should clarify what this observable is intended to probe (for example, lepton-flavor universality in the chiral structure of the current, or NP models with different operator combinations) and specify what size of deviation from the SM would constitute evidence.
minor comments (5)
  1. [Sec. 3.3] The sentence 'the left-handed scalar operator O_SR introduces slight shape modifications' contains a wrong chirality label; O_SR is the right-handed scalar operator. This appears to be a typo but should be corrected.
  2. [Sec. 2.3, around Eq. (65)] The phrase 'the rest frame of the off-shell Woff − shell' appears garbled; it should read 'the rest frame of the off-shell W' or similar.
  3. [Sec. 3.2, after Eq. (97)] The text says 'It can seen that there is little deviation'; 'can seen' should be 'can be seen.'
  4. [Table 4 and Table 5] The tables compare many models, but the caption and text do not state which uncertainties are included in each model's errors; for the models without uncertainties (e.g., CQM, RQM, CCQM, NRQM in Table 5) the absence of errors should be noted explicitly.
  5. [Figure 4 caption] The caption says 'red line and blue one are for Λ_c^+ → Λ ℓ^+ν_ℓ and Λ_c^+ → nℓ^+ν_ℓ, respectively,' but the color assignment appears reversed relative to the text in Sec. 3.2 ('the blue lines correspond to the decay Λ_c^+ → μℓ^+ν_ℓ, while the red lines represent Λ_c^+ → nℓ^+ν_ℓ'). Please check and harmonize the figure and text.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity; the SM predictions are independent given external lattice form factors, and the NP benchmark is a disclosed upper-bound scenario rather than a fitted prediction.

full rationale

The central SM derivation is self-contained with respect to the paper's own inputs: the branching fractions in Eqs. (92)-(99) are obtained by inserting external lattice QCD form factors [21,45] into the helicity-amplitude framework of Secs. 2.3-2.4, with no experimental Lambda_c branching fraction used as input, so the roughly 10% SM excess is a genuine prediction, not a fit. The NP analysis in Sec. 3.3 is also not circular in the strict sense: the quoted Wilson-coefficient fits [18,56,22] use D and D_s data, not Lambda_c data, and the Lambda_c observables are evaluated as functions of those coefficients. The authors' own Ref. [18] is cited only for order-of-magnitude guidance, and the actual numerical benchmark in Eq. (102) is explicitly adopted 'in order to maximize the manifestation of new physics effects', so the resulting 'up to 10%' suppression is a transparent upper-bound illustration rather than a fitted prediction; the abstract's phrase 'Using Wilson coefficients fitted from D and D_s meson decays' is imprecise but does not make the derivation circular. The A_mu/e_FB ratio is a derived observable whose hadronic uncertainties cancel by construction, and its insensitivity to the adopted NP operators is a numerical finding, not an input. The main caveats are external-input dependence on the lattice form factors and an internal sign/consistency tension (the summary favors negative C_SR while Eq. (102) adopts positive C_SR = 0.3); these are correctness risks, not circularity.

Assumptions & free parameters 7 free parameters · 4 assumptions · 0 invented entities

The analysis leans on two external pillars: lattice QCD form factors for the hadronic matrix elements, and Wilson coefficients fitted in meson decays. Both are standard inputs, but neither is derived in this paper. No new particles or forces are introduced.

free parameters (7)
  • C_VL = 0.03
    Adopted from fits to D and D_s decays in Refs. [18,22,56]; not re-fitted here and no uncertainty propagated.
  • C_VR = -0.01
    Adopted from the same prior fits; used in Eqs. (102) and in Figures 5 and 6.
  • C_SL = 0.3
    Adopted to maximize the manifestation of new physics effects; value sits near the boundary of the fits in Refs. [18,56].
  • C_SR = 0.3
    Adopted for the right-handed scalar operator; drives the claimed up-to-10 percent suppression in Lambda_c to (Lambda, neutron) mu nu.
  • C_T = 0.15
    Adopted for the tensor operator; used only for the Lambda_c to neutron mode because tensor form factors for Lambda_c to Lambda are unavailable.
  • Lattice form factor coefficients for Lambda_c to Lambda = Nominal fit values in Table 2
    Taken from Meinel lattice QCD [21]; these fit coefficients determine the central values and uncertainties of all SM predictions for the Lambda mode.
  • Lattice form factor coefficients for Lambda_c to neutron = Nominal fit values in Table 3
    Taken from Meinel lattice QCD [45]; these coefficients determine the SM predictions for the neutron mode and the tensor-operator contributions.
assumptions (4)
  • domain assumption No right-handed neutrinos in the effective Hamiltonian
    Stated in Sec. 2.1; restricts the operator basis to five operator types.
  • domain assumption The lattice QCD form factors from Refs. [21,45] correctly describe the Lambda_c to Lambda and Lambda_c to neutron hadronic matrix elements
    Used throughout Secs. 2.2 and 3.2; all numerical results inherit these inputs.
  • domain assumption Wilson coefficients fitted in D and D_s meson decays apply unchanged to Lambda_c decays via the same short-distance c to (s,d) l nu operators
    Assumed in Sec. 3.3 when transferring the fit results of Refs. [18,22,56] to the baryon decays.
  • standard math The z-expansion parameterization converges with the fitted truncation order
    Eq. (11) with n up to 3 in Tables 2 and 3; the higher-order fit is used to estimate systematic uncertainty.

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Cite this review

Pith. "Pith review of Investigation of $\Lambda_c \to (\Lambda,n)\ell^+ \nu_\ell $ Decays in Standard Model and Beyond." pith.science (2026). https://pith.science/paper/HPFVEOUQ

@misc{pith2026250112871,
  author       = {Pith},
  title        = {Pith review of: Investigation of $\Lambda_c \to (\Lambda,n)\ell^+ \nu_\ell $ Decays in Standard Model and Beyond},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HPFVEOUQ}},
  note         = {Machine review of arXiv:2501.12871}
}
abstract

In this work, we study the decays $\Lambda_c \to (\Lambda, n) \ell^+ \nu_\ell$ ($\ell = \mu, e$) within a model-independent framework. We calculate the helicity amplitudes for all possible four-fermion operators, including the interactions between different new physics (NP) operators. The form factors for the $\Lambda_c \to (\Lambda, n)$ transitions are taken from lattice QCD calculations. We present detailed results for the branching fractions and other key observables. Although our results are generally consistent with previous studies, we find that the predicted central values for the branching fractions are approximately $10\%$ larger than the experimental measurements. Additionally, we explore the potential impacts of NP, focusing particularly on the scenario in which NP particles couple exclusively to the muon. Using Wilson coefficients fitted from $D$ and $D_s$ meson decays, we examine NP effects in the $\Lambda_c \to (\Lambda, n) \mu^+ \nu_\mu$ decay channels. It is found that although most potential contributions of NP are obscured by the uncertainties inherent in both theory and experiment, the right-handed scalar operator could suppress the branching fraction of $\Lambda_c \to (\Lambda, n) \mu^+ \nu_\mu$ by up to $10\%$. We also highlight that the ratio of the forward-backward asymmetry in the $\Lambda_c \to (\Lambda, n) \mu^+ \nu_\mu$ decay to that in the $\Lambda_c \to (\Lambda, n) e^+ \nu_e$ decay provides a novel probe for NP, as it is less sensitive to hadronic uncertainties and is largely unaffected by current NP operators. All of our results can be tested in ongoing experiments such as BESIII, Belle-II, and LHCb, as well as in future high-energy facilities like the Super Tau-Charm Factory (STCF) and the Circular Electron Positron Collider (CEPC).

Figures

Figures reproduced from arXiv: 2501.12871 by the authors.

Figure 1
Figure 1. Definition of the polar and the azimuthal angles. [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. The q 2 -dependence of the differential branching ratios dB/dq2 , the forward-backward asymmetries on the leptonic side AF B(q 2 ), the convexity parameters C ℓ F (q 2 ), and the helicity asymmetries of the final baryons and leptons for the decays Λ+ c → Λℓ +νℓ , respectively. In all figures, the red lines with orange bands are for muon mode, and the the blue lines with green bands are for electron mode. are collect… view at source ↗
Figure 3
Figure 3. The q 2 -dependence of the differential branching ratios dB/dq2 , the forward-backward asymmetries on the leptonic side AF B(q 2 ), the convexity parameters C ℓ F (q 2 ), and the helicity asymmetries of the final baryons and leptons for the decays Λ+ c → nℓ+νℓ, respectively. In all figures, the red lines with orange bands are for muon modes, and the the blue lines with green bands are for electron modes. are larger … view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The q 2 -dependence of ratio R µ/e B (q 2 ) and A µ/e B (q 2 ), where red line and blue one are for Λ+ c → Λℓ +νℓ and Λ+ c → nℓ+νℓ, respectively. Specifically, the forward-backward asymmetry AF B approaches zero for the decay Λ+ c → Λ(n)e +νe as q 2 → 0, while it tends…
Figure 5
Figure 5. Figure 5: The q 2 -dependence of differential ratios dBr/dq2 , the R value, the forward-backward asymmetries of the leptonic side AF B(q 2 ), the convexity parameters C ℓ F (q 2 ), and the transverse polarization components of the Λ and leptons of Λ+ c → Λµ +νµ with NP operators…
Figure 6
Figure 6. Figure 6: The q 2 -dependence of differential ratios dBr/dq2 , the R value, the forward-backward asymmetries of the leptonic side AF B(q 2 ), the convexity parameters C ℓ F (q 2 ), and the transverse polarization components of the n and leptons of Λ+ c → nµ+νµ with NP operators …

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.